1. Field of the Invention
The invention generally relates to the field of short optical pulse characterization and, more particularly, to characterizing optical pulses using chronocyclic tomography.
2. Description of the Related Art
In optical communications systems, it is necessary to characterize the phase and amplitude of optical pulses as accurately as possible in order to predict and mitigate signal degradation. For example, in long distance wavelength-division multiplexed (WDM) systems, transmitted optical signals are subjected to nonlinear effects, such as self-phase modulation or cross-phase modulation, which degrade the transmission properties of the optical signals. By characterizing received optical pulses, an optical communication system may employ corrective measures to compensate for the effect of the distortions on a propagating optical signal.
As the need for information increases, so does the demand for higher speed and higher capacity communication systems. Higher speed communication systems result in both shorter optical pulses for transmission at higher bit rates (e.g., approximately 8 ps pulses for 40 Gb/s systems), and fast optical components to process the higher bit rate optical signals. As optical pulses are now used that are shorter in duration than the response time of the fastest available photodetectors, optical communications systems require more elaborate diagnostics to characterize the optical pulses.
One approach to characterizing short optical pulses involves the use of tomographic techniques to reconstruct the electric field of an optical pulse. The Wigner-Ville (W-V) distribution of a short optical pulse is a time frequency distribution. The action of all filters or measurement devices on a short pulse can be expressed as mathematical operations on its Wigner function. A typical example is that measuring the optical spectrum of the pulse is equivalent to projecting the Wigner-Ville function of the pulse on the frequency axis. Tomographic techniques use several projections, i.e. the projections on several different axes, to reconstruct the W-V function and the electric field of the pulse. The most general tomographic technique uses a large number of projections of the W-V distribution on various axes and reconstructs the electric field using a back projection algorithm (referred to herein as the “complete chronocyclic technique”). It is mathematically equivalent to project the W-V function on various axes or to rotate the W-V function and project it on a fixed axis. However, the latter is easier experimentally, since a spectrometer may be used to project the W-V function on the frequency axis and an arbitrary rotation of the W-V distribution may be implemented in chronocyclic space by combining quadratic spectral phase modulation and a quadratic temporal phase modulation. However, using the complete chronocyclic technique to characterize optical pulses is undesirable, since a large rotation of the W-V function requires a large bandwidth. In addition, since the complete chronocyclic technique requires many projections of the W-V distribution, the complete chronocyclic technique requires the measurement of a large number of one-dimensional spectra to obtain the one-dimensional electric field of an optical pulse under test.
In another tomographic approach, only two projections of the W-V function are used: the frequency marginal (i.e., the spectral intensity of the optical pulse), and the time-marginal (i.e., the temporal intensity of the optical pulse) (referred to herein as the “time-to-frequency conversion technique”). The time marginal is obtained by rotating the W-V function by π/2 radians and measuring the spectrum of the resulting field. The time-to-frequency conversion technique, however, still requires a large bandwidth due to the large rotation of the W-V function. In addition, the time-to-frequency conversion technique does not adequately yield the electric filed, since the retrieval of the electric field from the spectral and temporal intensities is ambiguous.